This proverb, "There is death in the hane", refers to the fact that the hane is a very common method of killing groups. The main purpose of the hane is to reduce the space for making eyes.
The hane at kills the Black group with a bulky five dead shape. If Black tries to capture at a, this does not gain an eye, and White can block Black's escape at b.
For example, this Black group (an L+1-group) can be killed with the hanes at and
. If Black blocks at a, it will turn Black's interior space into a dead bulky five. White can then kill Black with a placement tesuji at b.
Notice that in the above examples, the hane stone is not defended when put into atari. Instead another hane or a placement follows. That is because the capturing the hane stone will get a false eye.